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1. C) (4, 5)

              2. D) (3, 4)

              3. B) 5/2

Step-by-step explanation:

Plug in the (x, y) coordinates to see which makes a true statement for both of the given inequalities.

             y ≥ -2x + 11               and                 y > 3x - 9

A) (2, 1)   1 ≥ -2(2) + 11   → 1 ≥ 7 is false

B) (4, 1)   1 ≥ -2(4) + 11   → 1 ≥ 3 is false

C) (4, 5) 5 ≥ -2(4) + 11   → 5 ≥ 3 is TRUE    5 > 3(4) - 9  → 5 > 3 is TRUE

D) (6, 6) 6 ≥ -2(6) + 11   → 6 ≥ -1 is TRUE   6 > 3(6) - 9  → 6 > 9 is false

The only option that produces a TRUE statement for both inequalities is C

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Given (2, 6), the k-value is 2 · 6 = 12.

Which (x, y) coordinates have a product of 12?

A) (1, 3) --> 1 · 3 = 3

B) (1, 4)  --> 1 · 4 = 4

C) (3, 3) --> 3 · 3 = 9

D) (3, 4) --> 3 · 4 = 12      THIS WORKS!

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In order for the equation to have infinite solutions, the left side must equal the right side.  Solve for "c"

8x - 2x(c + 1) = x

     -2x(c + 1) = -7x               subtracted 8x from both sides

           c + 1 = (-7x)/(-2x)      divided both sides by -2x

           c + 1 = 7/2                simplified

           c      = 5/2                subtracted 1 from both sides